Editing Electrogravitics (section)

=== Components ===

The components of the stress-energy tensor describe various aspects of the electromagnetic field's influence on spacetime, including energy density, momentum density, and stress.

==== Other Versions ====

There are alternative formulations of the stress-energy tensor for specific applications or contexts. These versions may involve different physical quantities or mathematical expressions depending on the problem at hand. Examples include formulations for specific materials, boundary conditions, or energy-momentum distributions.

===== Examples =====

* Stress-energy tensor for a material medium, incorporating the effects of material properties such as conductivity, permittivity, and permeability.
<math>
T^{\mu\nu} = \varepsilon_0 \left( E^\mu E^\nu - \frac{1}{2} g^{\mu\nu} E_\alpha E^\alpha \right) + \frac{1}{\mu_0} \left( B^\mu B^\nu - \frac{1}{2} g^{\mu\nu} B_\alpha B^\alpha \right)
</math>

* Stress-energy tensor for an electromagnetic field in the presence of matter, accounting for the interaction between electromagnetic fields and matter fields.
<math>
T^{\mu\nu} = \frac{1}{\mu_0} \left( F^{\mu\lambda} F^\nu{}_\lambda - \frac{1}{4} g^{\mu\nu} F_{\alpha\beta} F^{\alpha\beta} \right) + T^{\mu\nu}_{\text{matter}}
</math>

* Stress-energy tensor for an electromagnetic field in a curved spacetime, considering the gravitational effects on the electromagnetic field.
<math>
T^{\mu\nu} = \frac{1}{\mu_0} \left( F^{\mu\lambda} F^\nu{}_\lambda - \frac{1}{4} g^{\mu\nu} F_{\alpha\beta} F^{\alpha\beta} \right) - \frac{1}{4\pi} \left( R^{\mu\nu} - \frac{1}{2} g^{\mu\nu} R \right)
</math>

* Stress-energy tensor for an electromagnetic field in a non-inertial frame of reference, incorporating effects such as acceleration and rotation.
<math>
T^{\mu\nu} = \frac{1}{\mu_0} \left( F^{\mu\lambda} F^\nu{}_\lambda - \frac{1}{4} g^{\mu\nu} F_{\alpha\beta} F^{\alpha\beta} \right) - \frac{1}{c^2} \left( F^{\mu\lambda} a_\lambda^\nu + F^{\nu\lambda} a_\lambda^\mu \right)
</math>

These equations demonstrate the versatility of the stress-energy tensor and its adaptability to different physical scenarios.